Reset control systems: stabilization by nearly-periodic reset

Laurentiu Hetel (1) , Jamal Daafouz (2) , Sophie Tarbouriech (3) , Christophe Prieur (4)

1 SyNeR - Systèmes Non Linéaires et à Retards
2 CRAN - Centre de Recherche en Automatique de Nancy
3 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
4 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité

In this paper the class of linear impulsive systems is considered. These systems are those with a continuous linear dynamics for all time, except at a sequence of instants. When such a discrete time occurs, the state undergoes a jump, or more precisely follows a discrete linear dynamics. The sequence of time instants, when a discrete dynamics occurs, is nearly- periodic only, i.e. it is distant from a periodic sequence to an uncertain distance. This paper succeeds to state tractable conditions to analyze the stability, and to design reset matrices such that the hybrid system is globally asymptotically stable to the origin. The approach is based on a polytopic embedding of the uncertain dynamics. An example illustrates the main stability result.

Domaines: Automatique / Robotique

Laurentiu Hetel, Jamal Daafouz, Sophie Tarbouriech, Christophe Prieur. Reset control systems: stabilization by nearly-periodic reset. IFAC WC 2011 - 18th IFAC World Congress, Aug 2011, Milan, Italy. p. 2395-2400. ⟨hal-00573989⟩